Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2501.06967

Stability analysis of solutions in the helicoidal Peyrard-Bishop model of DNA molecule

Anna Batova·Dragana Ranković·Slobodan Zdravković
View original source ↗Read source document ↗Export metadata ↓

Abstract

We use the helicoidal Peyrard-Bishop model of DNA in the current work. We solve a dynamical equation of motion using a continuum approximation, resulting in kink-solitary waves that travel along the chain. We demonstrate that, whereas supersonic kink solitons are not stable, subsonic ones are. Moreover, we demonstrate the importance of viscosity by showing that no wave is stable in the absence of viscosity.

Explore related subjects

physics.bio-ph

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Anna Batova, Dragana Ranković, Slobodan Zdravković. 2025-01-12. Stability analysis of solutions in the helicoidal Peyrard-Bishop model of DNA molecule. https://arxiv.org/abs/2501.06967

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Signature of mechanically induced cell extrusions in cell size distribution

How a growing tissue organizes its own homeostatic state is a central question in the physics of living matter. We show that when a growing epithelial sheet counteracts increasing cell density by mechanically squeezing cells out of its plane, a homeostatic in-plane pressure emerges as a generalization of a yield stress. We find that in the quasistatic growth limit the homeostatic state is marginally stable, with a pseudogap in the distribution of local distances to the extrusion threshold pressure. Because such mechanically induced extrusions arise from an instability of individual cells, the pseudogap is imprinted in the distribution of cell areas. This provides an image-based way to test for presence of mechanically induced extrusions and we identify this signature in the developing wing epithelium of \textit{D.~melanogaster}. We expect the same principles to apply to confined three-dimensional tissues.

physics.bio-ph↗
arXiv2026

Fluidization in Growth-Induced Morphogenesis

Elastic buckling has explained shape formation in growing tissues, yet the role of tissue fluidity remains elusive. We derive a minimal fluidized growth-elasticity model as a nonlinear analogue of Maxwell rheology. Analysis of a growing strip reveals a different picture of growth-induced morphogenesis: rather than emerging at a critical stress, symmetry breaking develops continuously during growth. Fluidity regulates stress evolution, the rate of shape-symmetry breaking, and flow patterns, establishing it as an active regulator of morphogenesis beyond its intuitive role in stress relaxation.

physics.bio-ph↗
arXiv2026

The Motile-Units model: Interacting spins model of cell polarization and motility

We introduce a coarse-grained interacting-spin model for two-dimensional cell motility, in which the cell perimeter is discretized into stochastic binary spins that switch between active and inactive states. Each perimeter spin represents a "motile-unit" that is a source of protrusive force and retrograde flow when active. Long-range interactions between the motile-units arise through a polarity cue advected by the collective actin retrograde flow, providing a minimal realization of spontaneous symmetry breaking and self-propulsion. The model exhibits three dynamical phases, a random walk phase, persistent random walk phase, and an intermittent bistable phase characterized by run-and-tumble migration. Additional nearest-neighbor interactions modulate speed and persistence without altering the overall phase structure. Owing to its simplicity, the framework naturally incorporates external cues, reproducing chemotactic migration, steering by localized optogenetic activation, and directional decision-making (symmetry breaking) under competing stimuli. The model introduces a new class of active-particle model in which both speed and polarity emerge from internal stochastic spin dynamics, rather than being imposed as particle-level variables, offering a framework for the study of cell migration and extends the scope of active-matter physics.

physics.bio-ph↗